Does leaving a wedding ring makes him guilty!? Absolutely not.
In the mind of a die hard LN it most certainly does..... They are so obsessed with Oswald being a lone nut shooter, that him leaving a light on is for them conclusive evidence of guilt
Among all the people at Dealey Plaza at 12:30PM, Oswald was probably the only one person of interest due to his life in USSR. If you would line them all together, you would only pick him for further interrogation. He was aware of this and he run away even he had nothing to do with it.
OK, he left the ring and the money, probably expecting he will be apprehended and questioned.
Still, you come to a gun question, why did he take the gun? He was in a great fear and could not think clearly.
All in all, when you take everything into the consideration, it is very hard to accept he did it as a LN.